Why can't there be common terms on both complementary function and particular integral when solving differential equations?(adsbygoogle = window.adsbygoogle || []).push({});

For instance,

dy/dx + 3y = exp(-x) + exp(-3x)

y(CF) = Aexp(−3x)

y(PI) = Cexp(−x) + Dxexp(−3x)

The term Dexp(-3x) in the P.I. has to be multiplied byxto be linearly independent of Aexp(-3x) in the C.F.. Why? What would happen if it wasn't?

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# Special case when solving D.E.'s

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